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# ltqnorm - function z = ltqnorm(p%LTQNORM Lower tail...

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function z = ltqnorm(p) %LTQNORM Lower tail quantile for standard normal distribution. % % Z = LTQNORM(P) returns the lower tail quantile for the standard normal % distribution function. I.e., it returns the Z satisfying Pr{X < Z} = P, % where X has a standard normal distribution. % % LTQNORM(P) is the same as SQRT(2) * ERFINV(2*P-1), but the former returns a % more accurate value when P is close to zero. % The algorithm uses a minimax approximation by rational functions and the % result has a relative error less than 1.15e-9. A last refinement by % Halley's rational method is applied to achieve full machine precision. % Author: Peter J. Acklam % Time-stamp: 2003-04-23 08:26:51 +0200 % E-mail: [email protected] % URL: http://home.online.no/~pjacklam % Coefficients in rational approximations. a = [ -3.969683028665376e+01 2.209460984245205e+02 ... -2.759285104469687e+02 1.383577518672690e+02 ... -3.066479806614716e+01 2.506628277459239e+00 ]; b = [ -5.447609879822406e+01 1.615858368580409e+02 ... -1.556989798598866e+02 6.680131188771972e+01 ... -1.328068155288572e+01 ]; c = [ -7.784894002430293e-03 -3.223964580411365e-01 ... -2.400758277161838e+00 -2.549732539343734e+00 ... 4.374664141464968e+00 2.938163982698783e+00 ]; d = [ 7.784695709041462e-03 3.224671290700398e-01 ... 2.445134137142996e+00 3.754408661907416e+00 ]; % Define break-points. plow

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